A fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows

	Expected Return	Standard Deviation
Stock Fund	20%	30%
Bond Fund	12%	15%
The correlation between the fund returns is 0.1
rho	0.1
rf	8%

To answer the questions, please round the answers to two decimal places. For example, if you answer is 1.95%, please fill 1.95 in the slot. If you answer is 11.95%, please fill 11.95 in the slot. When the answer is a Sharpe ratio, don't use the percentage format. For example, you should fill in 0.58 in the slot if you get a Sharpe ratio of 0.58.

1. What is the covariance between the stock fund and the bond fund?

2. Suppose you invest in a portfolio with 60% in the stock fund and 40% in the bond fund. What is the expected return for your investment?

3. Suppose you invest in a portfolio with 60% in the stock fund and 40% in the bond fund. What is the standard deviation for your investment?

4. Suppose you invest in a portfolio with 60% in the stock fund and 40% in the bond fund. What is the Sharpe Ratio for your investment?

5. Find the global minimum variance portfolio (GMVP) using Excel Solver. What is the weight in the stock fund for your GMVP?

6. What is the standard deviation for your GMVP?

7. Find the tangency portfolio using Excel Solver. What is the weight in the stock fund for your tangency portfolio?

8. Suppose you are an investor with the utility function U = ER - 0.5A^2, and your risk aversion is 4. What is your optimal allocation in the stock funds?

9. Suppose you are an investor with the utility function U = ER - 0.5A^2, and your risk aversion is 2. What is your optimal allocation in the stock funds?

10. Suppose you are an investor with the utility function U = ER - 0.5A^2, and your risk aversion is 2. But your borrowing cost is 12%, rather than the risk-free rate 10%. What is your optimal allocation in the stock funds?